Functions and derivations of C1-algebras |
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Authors: | Alan McIntosh |
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Institution: | School of Mathematics and Physics, Macquarie University, North Ryde, N.S.W. 2113, Australia |
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Abstract: | It is shown that there is a closed symmetric derivation δ of a C1-algebra with dense domain (δ), an element A = A1 ?(δ), and a C1-function such that (A)?(δ). Some estimates are derived for , where 0 < α < 1. It is shown that there exists a family of one-one self-adjoint operators S(t) in (H) which depends linearly on t, while is not differentiable. It is also shown that there exists (H) which is not C1-self-adjoint even though it satisfies for all t ? |
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